Suppose the S&R index is 1000 and the dividend yield is zero. The continuously compounded borrowing rate is 5% while the continuously compounded lending rate is 4.5%. The maturity of the forward contract is 6 months.
(a) Suppose when you buy or sell the index, there is a transaction cost of $1 at t=0. There is also a transaction cost of $2 if you take a long or short forward position at t=0. There are no transaction costs on the maturity date. The futures price is 1026. Which of the statement is true?
A. You can do cash-and-carry arbitrage
B. You can do reverse cash-and-carry arbitrage
C. You can do both cash-and-carry and reverse cash-and-carry arbitrage
D. You cannot arbitrage
(b) Following part (a), what is the non-arbitrage upper bound of the forward price?
Answer is B
We can do REVERSE CASH AND CARRY ARBITRAGE
In that we need to :
1. Buy forward
2. Short sell asset
3. Invest that money
Forward price = 1026
Long Forward contract @1026
Transaction fee = 2
Short sell index and get 1000
Transaction fee = 1
Invest = 1000
interest = 4.5%
Amount after 1 year = 1000 * exp^0.045 = 1046.027
Total = 1046.027 - 2 - 1 = 1043.027
Settle the long position by paying 1026
So Profit = 1043.027 - 1026 = 17.027
Buy spot asset
short sell forward
Get Answers For Free
Most questions answered within 1 hours.